@article{Chen2023, 
author = {Yayun Chen and Tongzhu Li},
title = {Classification of spacelike conformal Einstein hypersurfaces in Lorentzian space              R        1          n      +      1},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23247-23271},
keywords = {conformal metric, conformal sectional curvature, conformal Einstein hypersurface, conformal transformation group},
url = {https://www.sciopen.com/article/10.3934/math.20231182},
doi = {10.3934/math.20231182},
abstract = {Let    f  :      M    n    →            R        1          n      +      1       be an    n-dimensional umbilic-free spacelike hypersurface in the    (  n  +  1  )-dimensional Lorentzian space              R        1          n      +      1       with an induced metric    I. Let    I  I be the second fundamental form and    H the mean curvature of    f. One can define the conformal metric    g  =      n          n      −      1        (  ‖  I  I      ‖    2    −  n      H    2    )  I on    f  (      M    n    ), which is invariant under the conformal transformation group of              R        1          n      +      1      . If the Ricci curvature of    g is constant, then the spacelike hypersurface    f is called a conformal Einstein hypersurface. In this paper, we completely classify the    n-dimensional spacelike conformal Einstein hypersurfaces up to a conformal transformation of              R        1          n      +      1      .}
}